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Finite Morse index solutions of exponential problems. (English) Zbl 1136.35030

Summary: We prove that the problem \(-\Delta u=e^u\) has no negative finite Morse index solution in \(\mathbb R^3\) and give some applications of this result to bounded domain problems.

MSC:

35J60 Nonlinear elliptic equations
47J30 Variational methods involving nonlinear operators
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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References:

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